Systems and methods for operating a MEMS device based on sensed temperature gradients

ABSTRACT

An exemplary microelectromechanical device includes a MEMS layer, portions of which respond to an external force in order to measure the external force. A substrate layer is located below the MEMS layer and an anchor couples the substrate layer and MEMS layer to each other. A plurality of temperature sensors are located within the substrate layer to identify a temperature gradient being experienced by the MEMS device. Compensation is performed or operations of the MEMS device are modified based on temperature gradient.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No.16/547,257 (now allowed), filed on Aug. 21, 2019. The disclosure of suchapplication is hereby incorporated by reference herein in its entirety.

BACKGROUND

Numerous items such as smartphones, smart watches, tablets, automobiles,aerial drones, appliances, aircraft, exercise aids, and game controllersutilize sensors during their operation (e.g., motion sensors, pressuresensors, temperature sensors, etc.). In commercial applications,microelectromechanical (MEMS) devices or sensors such as accelerometersand gyroscopes capture complex movements and determine orientation ordirection. For example, smartphones are equipped with accelerometers andgyroscopes to augment navigation systems that rely on Global PositionSystem (GPS) information. In another example, an aircraft determinesorientation based on gyroscope measurements (e.g., roll, pitch, and yaw)and vehicles implement assisted driving to improve safety (e.g., torecognize skid or roll-over conditions).

Each of the end-use products of MEMS devices involves placement adjacentto other electronic components, such as displays, processors, memory,antennas, and touchscreens. With the proliferation of MEMS devices inscores of different device types by different manufactures, heatdispersion from adjacent components can be unpredictable as to theamount of heat dispersed from other components, the duration and patternof the heat dispersion, and the locations where heat is dispersed to theMEMS device. Furthermore, these numerous different types of devices areused in scores of end-use applications ranging from simple consumerelectronics to industrial environments and vehicles, furtherexacerbating the numerous heat dispersion profiles that MEMS devices mayendure during operation.

SUMMARY

In an embodiment of the present disclosure, a microelectromechanical(MEMS) device may comprise a first layer comprising a first planelocated within the first layer, a second layer comprising a second planelocated within the second layer, wherein the second layer is locatedbelow the first layer, and an anchor, wherein the anchor couples thefirst layer to the second layer. The MEMS device may comprise aplurality of temperature sensors located within the second plane,wherein each temperature sensor of the plurality of temperature sensorsis located at a different distance relative to the anchor. The MEMSdevice may comprise processing circuitry configured to output a signalthat corresponds to a thermal gradient perpendicular to the second planebased on an output of the plurality of temperature sensors.

In an embodiment of the present disclosure, a microelectromechanical(MEMS) device may comprise a first layer comprising a first planelocated within the first layer, wherein the first layer comprises atleast one proof mass, a second layer comprising a second plane locatedwithin the second layer, wherein the second layer is located below thefirst layer, and wherein the first layer and the second layer areseparated by a gap, and an anchor, wherein the anchor couples the firstlayer to the second layer and is at least partially located within thegap. The MEMS device may further comprise a plurality of temperaturesensors located within the second plane, wherein a first temperaturesensor of the plurality of temperature sensors is located below theanchor, and wherein a second temperature sensor of the plurality oftemperature sensors is not located below the anchor.

In an embodiment of the present disclosure, a method of operating amicroelectromechanical (MEMS) device may comprise receiving, from afirst temperature sensor located in a first layer proximate to ananchor, a first temperature signal, wherein the anchor is coupledbetween the first layer and a second layer within a gap between thefirst layer and the second layer. The method may further comprisereceiving, from a second temperature sensor located in the first layerat a distance further from the anchor than the first temperature sensor,a second temperature signal. The method may further comprisedetermining, by processing circuitry, a thermal gradient in thedirection of the second layer based on the first temperature signal andthe second temperature signal.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other features of the present disclosure, its nature, andvarious advantages will be more apparent upon consideration of thefollowing detailed description, taken in conjunction with theaccompanying drawings in which:

FIG. 1 shows an exemplary motion sensing system in accordance with someembodiments of the present disclosure;

FIG. 2A shows a side view of an exemplary MEMS device in accordance withsome embodiments of the present disclosure;

FIG. 2B shows a top view of a substrate layer of the MEMS device of FIG.2A in accordance with some embodiments of the present disclosure;

FIG. 3A shows an exemplary temperature sensing configuration inaccordance with some embodiments of the present disclosure;

FIG. 3B shows another exemplary temperature sensing configuration inaccordance with some embodiments of the present disclosure;

FIG. 3C shows another exemplary temperature sensing configuration inaccordance with some embodiments of the present disclosure;

FIG. 4 shows exemplary Wheatstone bridge processing circuitry inaccordance with some embodiments of the present disclosure; and

FIG. 5 shows exemplary steps for processing received temperature sensoroutputs in accordance with some embodiments of the present disclosure.

DETAILED DESCRIPTION OF DRAWINGS

An exemplary MEMS device may have a plurality of layers that arefabricated, patterned, and bonded together. A MEMS layer may be bondedbetween other layers (e.g., an upper or cap layer and a lower substratelayer) and may include one or more components that may move in responseto particular stimuli that are applied to the MEMS device. Electricalcircuitry of the MEMS device may interact with the micromechanicalcomponents to output signals of interest. For example, MEMS inertialsensors may include a suspended spring-mass system that is designed suchthat portions of the suspended spring-mass system (e.g., proof massessuspended within the suspended spring-mass system) move in a particularmanner in response to particular applied forces, such as linearacceleration along a measurement axis or angular velocity about ameasurement axis. An exemplary pressure sensor may have a cavity that ishermetically sealed with respect to one portion of the MEMS layer andanother cavity that receives a gas at another portion of the MEMS layer,resulting in movement of the MEMS layer based on the relative pressuresand MEMS layer design. Other exemplary devices that can be fabricatedusing MEMS techniques include magnetometers and ultrasonic sensors,although there are wide variety of devices such as sensors and actuatorsthat can be fabricated using MEMS techniques.

Because MEMS devices may be extremely small they are used in numerouselectronic devices, often in proximity to components that aresignificant heat sources, or in end-use applications where theenvironment includes significant heat sources. As a result, MEMS devicesmay be subject to a variety of heat conditions, resulting in significantvariances in relative location of exposure, time of exposure, rate ofchange over time, etc. As a result, MEMS devices may not be at a uniformtemperature and may instead experience complex thermal gradientsthroughout the device as a whole. These thermal gradients may also beimpacted by the design of the MEMS device itself, including thematerials of the respective layers, bonding materials between layers,configuration of bonding locations in which heat may transfer betweenlayers, intra-layer design such as MEMS layer design and locations anddensity of electrical components (e.g., within a CMOS substrate layer).

The thermal gradients may cause complex changes to the operation of thesensor, for example, by causing components within the MEMS layer toexpand or contract, modifying clearances between movable components,changing operating parameters of electrical components, and creatingpressure differentials within the cavity of the MEMS device. Because thethermal gradient may not be at a steady state, these effects may beexperienced differently by similar electrical and mechanical componentsat different relative locations within the sensor. Changing thermalgradients may result in Knudsen forces at boundaries where particles aretransferring energy therebetween, resulting in forces imparted onmechanical components such as proof masses. All of these changes due tothermal gradients may impact MEMS devices and components in complexways, and may degrade the precision and accuracy of the MEMS device.

One or more of the layers of the MEMS device (e.g., a CMOS substratelayer) may include electrical circuitry that can be located andconnected in a manner to measure and estimate thermal gradients,including complex thermal gradients transferred from other layers. Theelectrical circuitry can include components that are known to respond ina predetermined manner to temperature and/or changes in temperature,such as thermistors, Bipolar Junctions Transistors (BJTs)=, andMetal-oxide-semiconductor field-effect transistors (MOSFETs). Based onthe sensor design, these temperature-sensitive components (temperaturesensors) can be located and configured to detect and/or estimateparticular temperature gradients, both within the layer that they arelocated in and from other layers.

Heat from an external source is applied to the MEMS device at particularlocations along the periphery of the MEMS device, such as the top (e.g.,along top of the cap layer), sides (e.g., for a four-sided sensor, anyof four sides of the cap layer, MEMS layer, or CMOS layer, depending onthe location of the heat source), or bottom (e.g., along the bottom ofthe CMOS layer). These may be locations where heat is likely transferreddue to exposure to the external environment, circuit boards, or otherelectronic components. By placing temperature sensors at differentlocations relative to these edges within a particular layer (e.g., anelectrical component layer such as a CMOS layer), and in someembodiments within different component planes, the locations of heatsources as well as patterns of heat dispersion may be identified.

In an x-y-z coordinate system a MEMS layer may be bonded to and locatedabove the substrate layer in the positive z-direction while the caplayer may be bonded to and located above the MEMS layer in the positivez-direction. Connection points between these layers such as anchors thatinterconnect the MEMS layer and the substrate layer may be used toestimate thermal gradients outside of the substrate layer, as theselocations may exhibit relative changes in temperature within thesubstrate layer due to temperature dispersion from/to the MEMS layer viathe anchors. For example, temperature sensors located remote from theanchors within the substrate layer should have lower temperatures,assuming no in-plane thermal gradients are impacting the temperature.

Once thermal ingredients are identified, the information about thethermal gradients may be utilized to improve the operation of the MEMSdevice. In some embodiments, adjustments may be made to measured values,such as by changing scaling values, compensation codes, additivecompensation values, offsets, A/D conversion thresholds, amplifierinputs, and the like. Changes may also be made to the operation of theMEMS device, such as amplitude, phase or frequency of applied signals toMEMS layer or electrical components of the MEMS device. Identificationof thermal gradients may also be used to impact the operation of otherdevices, such as by sending alarms or warnings that may be used toadjust the operation of other electrical components that are adjacent tothe MEMS device, or to provide warnings to another system such as thatmeasurements may have lower accuracy or to allow the device to cool.Because of the ability of the temperature sensing system describedherein to identify and pinpoint complex thermal gradients, thecompensation or change in operation may be tailored to the specific typeand intensity of the thermal gradient.

FIG. 1 depicts an exemplary motion sensing system 10 in accordance withsome embodiments of the present disclosure. Although particularcomponents are depicted in FIG. 1 , it will be understood that othersuitable combinations of sensors, processing components, memory, andother circuitry may be utilized as necessary for different applicationsand systems. In an embodiment as described herein, the motion sensingsystem may include at least a MEMS device 12 and supporting circuitry,such as processing circuitry 14 and memory 16. In some embodiments, oneor more additional MEMS devices 18 (e.g., MEMS gyroscopes, MEMSaccelerometers, MEMS microphones, MEMS pressure sensors, and a compass)may be included within the motion processing system 10 to provide anintegrated motion processing unit (“MPU”) (e.g., including 3 axes ofMEMS gyroscope sensing, 3 axes of MEMS accelerometer sensing,microphone, pressure sensor, and compass).

Processing circuitry 14 may include one or more components providingnecessary processing based on the requirements of the motion processingsystem 10. In some embodiments, processing circuitry 14 may includehardware control logic that may be integrated within a chip of a sensor(e.g., on a substrate or cap of a MEMS device 12 or other MEMS device18, or on an adjacent portion of a chip to the MEMS gyroscope 12 orother MEMS device 18) to control the operation of the MEMS device 12 orother MEMS devices 18 and perform aspects of processing for the MEMSdevice 12 or other MEMS devices 18. In some embodiments, the MEMS device12 and other MEMS devices 18 may include one or more registers thatallow aspects of the operation of hardware control logic to be modified(e.g., by modifying a value of a register). In some embodiments,processing circuitry 14 may also include a processor such as amicroprocessor that executes software instructions, e.g., that arestored in memory 16. The microprocessor may control the operation of theMEMS device 12 by interacting with the hardware control logic, andprocess signals received from MEMS device 12. The microprocessor mayinteract with other sensors in a similar manner.

Although in some embodiments (not depicted in FIG. 1 ), the MEMS device12 or other MEMS devices 18 may communicate directly with externalcircuitry (e.g., via a serial bus or direct connection to sensor outputsand control inputs), in an embodiment the processing circuitry 14 mayprocess data received from the MEMS device 12 and other MEMS devices 18and communicate with external components via a communication interface20 (e.g., a SPI or I2C bus, or in automotive applications, a controllerarea network (CAN) or Local Interconnect Network (LIN) bus). Theprocessing circuitry 14 may convert signals received from the MEMSdevice 12 and other MEMS devices 18 into appropriate measurement units(e.g., based on settings provided by other computing units communicatingover the communication bus 20) and perform more complex processing todetermine measurements such as orientation or Euler angles, and in someembodiments, to determine from sensor data whether a particular activity(e.g., walking, running, braking, skidding, rolling, etc.) is takingplace.

In some embodiments, certain types of information may be determinedbased on data from multiple MEMS devices, in a process that may bereferred to as sensor fusion. By combining information from a variety ofsensors it may be possible to accurately determine information that isuseful in a variety of applications, such as image stabilization,navigation systems, automotive controls and safety, dead reckoning,remote control and gaming devices, activity sensors, 3-dimensionalcameras, industrial automation, and numerous other applications.

An exemplary MEMS device 12 may include one or more movable proof massesthat are configured in a manner that permits the MEMS device to measurea desired force (e.g., linear acceleration, angular velocity, magneticfield, etc.) along an axis. In some embodiments, the one or more movableproof masses may be suspended from anchoring points, which may refer toany portion of the MEMS device which is fixed, such as an anchor thatextends between a layer (e.g., a substrate or CMOS layer) that isparallel to the MEMS layer of the device, a frame of the MEMS layer ofthe device, or any other suitable portion of the MEMS device that isfixed relative to the movable proof masses. The proof masses may bearranged in a manner such that they move in response to measured force.The movement of the proof masses relative to a fixed surface (e.g., afixed sense electrode extending into the MEMS layer or located parallelto the movable mass on the substrate) in response to the measured forceis measured and scaled to determine the desired inertial parameter.

Heat sources from adjacent components (e.g., processors, power sources,transponders, etc.) or from the external environment may cause heatdispersion to a portion of the MEMS sensor. When this dispersion of heatgenerates a thermal gradient along any of the x-axis, y-axis, or z-axis,or combinations thereof, air pressure within the cavity may becomeunbalanced, based on the different relative temperatures at differentportions of the cavity. This may cause the proof masses to move a fixeddistance (e.g., corresponding to the pressure differential) relative tothe electrodes, resulting in an offset in the sensed capacitance. Thisoffset is unrelated to the measured parameter and may reduce theaccuracy of measurements.

FIG. 2A shows a side view of an exemplary MEMS gyroscope in accordancewith some embodiments of the present disclosure. Although the presentdisclosure will discuss thermal gradient sensing and compensation in thecontext of a gyroscope and a particular gyroscope design (e.g., anout-of-plane sensing gyroscope with a plurality of centrally located andevenly spaced anchors), it will be understood that the temperaturesensors, configurations, and compensation described herein may beapplied to a variety of suitable MEMS or other semiconductor deviceswhere thermal gradient is desired to be measured. As described herein,temperature sensors may be located in relative locations with respect tokey heat dispersion points (e.g., anchors, bond points, vias, exposedsidewalls, etc.) in order to accurately identify different thermalgradients of interest. Based on the principles described herein, it willbe understood that the temperature gradient sensing and compensationtechniques described herein may be applied to numerous device types anddesigns. In some embodiments, the MEMS device 200 can be anaccelerometer, magnetometer, barometer, microphone or an ultrasonicsensor.

The MEMS device 200 of FIG. 2A may include a cap layer 202, MEMS layer204, and substrate layer 206, although in some embodiments additionallayers may be added or one or more layers may be substituted or removed.In an exemplary embodiment, the layers may be bonded together by bondinglayers 208A and 208B, with cap layer 202 bonded to MEMS layer 204 bybonding layer 208A and MEMS layer 204 bonded to substrate layer 206 bybonding layer 208B. Heat dispersion within and between these layers maydepend at least in part based on the respective materials of the caplayer 202.

The respective layers of the MEMS device 200 may be fabricated,patterned, bonded, and processed to generate a particular device ofinterest such as the MEMS gyroscope of FIG. 2A. In the exemplaryembodiment of FIG. 2A, a hermetically sealed cavity is formed and a MEMSgyroscope is located within the cavity. A gas is sealed within thecavity at a nominal pressure. The gas located within the cavity has itsown thermal properties depending on the gas, its nominal pressure, andthe shape of components within the cavity. For example, depending uponthe pattern of the thermal gradient experienced by the MEMS device andthe shape of the MEMS components of the gyroscope of FIG. 2A, certainthermal gradients such as a negative z-axis gradient TGz may result intemperature differentials for the gas at different locations in thecavity (e.g., based on proximity to heat sources and/or the interveningMEMS layer at least partially inhibiting heat dispersion betweenportions of the cavity). This may result in internal pressuredifferentials and Knudsen forces on the MEMS layer, which may in someinstances result in a fixed movement of movable MEMS components such asproof masses relative to the normal location of the proof masses.

The MEMS layer 204 may include a suspended spring-mass system 212, whichin the exemplary embodiment of FIG. 2A, comprises a MEMS gyroscope. Inthe exemplary embodiment of FIG. 2A, springs 210 couple the suspendedspring-mass system 212 to the bonded MEMS layer 204. The suspendedspring-mass system 212 includes a plurality of components that respondin a desired manner in response to a force to be sensed, such as byallowing proof masses 222, 224, 226, and 228 to move out-of-plane alongthe z-axis in response to an angular velocity about an in-plane axis. Inthe exemplary embodiment of FIG. 2A, a number of connecting arms and/orsprings 230, 232, and 234 couple the motion of the proof masses to eachother, such that respective masses 222/224 and 226/228 move inanti-phase in a similar manner.

Movement of the of the proof masses 222/224/226/228 may be sensed in avariety of suitable manners such as piezoelectric or capacitive sensing,although the exemplary embodiment of FIG. 2A depicts electrodes240/242/244/246 patterned on the substrate, each forming a respectivecapacitor with a respective one of the proof masses having a capacitancethat changes based on the distance between the electrode and proof mass(e.g., a capacitor of proof mass 222 and electrode 240, a capacitor ofproof mass 224 and electrode 242, a capacitor of proof mass 226 andelectrode 244, and a capacitor of proof mass 228 and electrode 246).Thermal gradients may cause changes to the distance between the proofmasses and the electrodes as described herein, which may result inadditive and/or periodic changes to the sensed capacitance and thus themeasured value (e.g., angular velocity).

As described herein, heat sources may apply a thermal gradient to someportion of the MEMS device 200, for example, via contact or proximity toany of the sides of the MEMS device 200. The pattern of heat dispersionwithin the MEMS device 200 depends on the nature of the heat source(e.g., point or distributed), the location where the heat source isapplied, the material properties of the various portions of the MEMSdevice, the design of the cavity and device components, and otherfactors as described herein. For simplicity of demonstration, thepresent discussion will refer to thermal gradients having componentsalong the out-of-plane z-axis (i.e., TGz) and within the x-y plane(i.e., TGx and TGy). However, it will be recognized that in someinstances there may be multiple significant heat sources applied atdifferent portions of the MEMS device, such that multiple thermalgradients disperse throughout the MEMS device in different patterns andinteract at locations within the MEMS device (e.g., at least until asteady state temperature is reached after a lengthy period of exposureto the multiple significant heat sources).

In an exemplary embodiment as depicted in FIG. 2A, the cap layer 202,MEMS layer 204, and substrate layer 206 are not only bonded to eachother at the exterior of the MEMS device 200, but are also coupled viaanchors 214, 216, 218, and 220. Anchors 218 and 220 couple cap layer 202to MEMS layer 204 and anchors 214 and 216 couple MEMS layer 204 tosubstrate layer 206. These anchors provide heat dispersion paths throughwhich thermal gradients propagate between the respective layers at agreater rate than via the gas of the cavity. The anchors thus providefor heat dispersion between the respective layers in the out-of-plane(z-axis) direction, and are representative of the z-axis thermalgradient TGz (e.g., with the magnitude of thermal gradients based on theanchor locations, size, and material).

In some embodiments of the present disclosure, temperature sensors maybe located on or within one or more of the layers of the MEMS device.For example, many electronic components such as resistors, thermistors,BJTs, MOSFETs, and thermocouples may have known responses to temperaturethat can be monitored. In an exemplary embodiment, some of thesetemperature sensors may be located within a layer of the MEMS devicethat allows for the creation and monitoring of temperature sensors, suchas a CMOS substrate layer 206.

Although it will be understood that any suitable layer havingappropriate materials and processes to form electronic components (e.g.,the patterning of thermistors, thermocouples, or other components withinsemiconductor layers), in the exemplary embodiment of FIG. 2A the CMOSsubstrate layer 206 includes multiple planes (i.e., x-y planes) on whichelectronic components may be formed. For example, temperature sensors260, 262, 264, and 266 may be located in a first x-y plane relativelycloser to the upper plane of the CMOS substrate layer 206. Temperaturesensors 270, 272, 274, and 276 may be located in a second x-y plane thatis further away from the upper plane of the CMOS substrate layer 206.Although particular depths are depicted in FIG. 2A, it will beunderstood that a number of different temperature sensor depths (e.g.,planes for temperature sensors) may be utilized in embodiments of thepresent disclosure.

The temperature sensors may be located at respective locations tocapture particular information of interest, such as temperatureproximate to the anchors 214 and 216 (e.g., temperature sensors 260 and266), temperature proximate to electrodes (e.g., temperature sensor 270for electrode 240, temperature sensors 262 and 272 for electrode 242,temperature sensors 264 and 274 for electrode 244, and temperaturesensor 276 for electrode 246), temperature proximate to the edges of theMEMS device 200 (e.g., temperature sensors 270 and 276), andtemperatures located near the interior of the MEMS device (e.g.,temperature sensors 262, 264, 272, and 274).

Temperature sensors may also be located at locations on the surface oflayers at the interior or exterior of the MEMS device 200. Although avariety of temperature sensors may be located at a variety of locationson the surface of layers, in an exemplary embodiment thermistors and/orthermocouples may be patterned on the surface of layers of the MEMSdevice, to form temperature sensor 250 and 256 located on an exteriorsurface of the MEMS layer 204 and temperature sensors 252 and 254located on a top surface of cap layer 202.

FIG. 2B shows a top view of a substrate layer of the MEMS gyroscope ofFIG. 2A in accordance with some embodiments of the present disclosure.In the exemplary embodiment of FIG. 2B, the locations of the temperaturesensors are depicted in a particular configuration in respective x-yplanes within the substrate, with the temperature sensors 260A, 260B,260C, 262A, 262B, 264A, 264B, 266A, 266B and 266C located within a firstx-y plane at a first depth below the depicted upper surface of thesubstrate. The temperature sensors 270A, 270B, 272A, 272B, 274A, 274B,276A, and 276B are located within a second x-y plane at a second depthbelow the depicted upper surface of the substrate, with the second planebeing located at a greater z-direction depth than the first plane.Although particular sensor locations and a particular number of sensorsare depicted in FIGS. 2A and 2B, it will be understood that the sensorlocations and quantity of sensors may be varied in accordance with thepresent disclosure based on factors such as MEMS device design, likelylocations of heat sources, anchor locations, and the like. And althoughthe temperature sensors of FIGS. 2A and 2B are depicted in two x-yplanes at respective z-axis depths within the substrate layer 206, thetemperature sensors may be located on a single plane or on more than twoplanes, or on planes that are not normal to the z-axis of the MEMSdevice.

The top view of FIG. 2B depicts the locations where the anchors 214 and216 contact and attach to the substrate layer 206, creating a path forthermal gradients to pass between MEMS layer 204 and substrate layer206. Electrodes 240, 242, 244, and 246 are depicted in FIG. 2B asoverlying the substrate layer 206. In the exemplary embodiment of FIGS.2A and 2B, the temperature sensors are located at relative locationswith respect to the primary heat sources, such as the edges of thesubstrate layer 206 and the anchor locations 214 and 216. In someembodiments, the design and materials for the electrodes 240, 242, 244,and 246 may be such that the electrodes may also function as heatsources for the substrate layer 206 under certain conditions.

In the exemplary embodiment of FIGS. 2A and 2B, the temperature sensorsare located in a manner such that a variety of temperature data may beobtained, although it will be understood that different numbers oftemperature sensors may be placed at different locations, based onsensor design (e.g., anchor and electrode locations, and likelylocations of heat sources based on end uses and/or insulating packaginglocated proximate to one or more of the sides of the MEMS device) andother factors (e.g., types of temperature sensors available andlocations suitable for placement of temperature sensors). In theexemplary embodiment of FIGS. 2A and 2B, temperature sensors may belocated at different locations with respect to the edges of the sensoralong the x and y axes. A heat source applied along the y-axis at theedge closest to electrode 240 and a cold source along the y-axis on theopposite side will result in a thermal gradient TGy and differential(i.e., decreasing) temperature outputs depending on temperature sensorlocation relative to the thermal gradient and heat source (i.e., zerorelative temperature at 302 with the temperature sensed by temperaturesensors 270A/270B and 276A/276B being equal and opposite in magnitude,temperature sensors 260A/260B/260C and 266A/266B/266C being equal andopposite in magnitude, and temperature sensors 272A/272B and 274A/274Bbeing equal and opposite in magnitude.) Swapping the locations of theheat source and cold source along the y-axis (e.g., such that the heatsource closest to electrode 246) will result in similar temperaturesensor outputs with zero relative temperature change at 302.

A heat source applied along the x-axis at the edge closest totemperature sensors 270B, 262B, 264B, and 276B along with a cold sourceapplied at the opposite side will result in a thermal gradient TGx anddifferential (i.e., zero relative temperature at 302 and 260B/266Btemperature outputs depending on the location of temperature sensorsrelative to the thermal gradient and heat source (i.e., such that theoutputs of the temperature sensors 262B/264B and 262A/264A being equaland opposite in magnitude, temperature sensors 270B/276B and 270A/276Abeing equal and opposite in magnitude, temperature sensors 272B/274B and272A/274A being equal and opposite in magnitude, temperature sensors260C/266C and 260A/266A being equal and opposite in magnitude). Swappingthe heat source and cold source along the x-axis (e.g., such that theheat source is closest to temperature sensor 270A, 262A, 264A, and 276A)will result in similar temperature sensor outputs with zero relativetemperature at 260B/266B and 302.

A heat source applied along the z-axis originating from one of thelayers above substrate layer 206 and a cold source on the opposite sideof substrate layer 206 will result in a thermal gradient TGz (depictedin FIG. 2A) and differential (i.e., decreasing) temperature outputsdepending on their location relative to the thermal gradient and heatsource. In an exemplary embodiment where temperature sensors are locatedon other layers (e.g., temperature sensors 252/254 on cap layer 202 andtemperature sensors 250 and 256 on MEMS layer 204), these temperaturesensors may experience a relatively large change in output compared tosome or all of the temperature sensors in the substrate layer 206 (e.g.,with the possible exception of temperature sensors260A/260B/260C/266A/266B/266C located proximate to the anchors 214 and216). The outputs of temperature sensors 250, 252, 254, and 256 willalso vary with respect to the exact location of the heat source withrespect to the cap layer 202 or MEMS layer 204.

In some embodiments of the present disclosure temperature sensors260A/260B/260C and 266A/266B/266C may be located within a plane of thesubstrate layer 206 below each of the anchoring regions 214 and 216 andtemperature sensors may be located within the plane of the CMOS layerremote from the anchoring regions. The temperature differences measuredbetween the locations may correspond to the dispersion of heat from theanchoring regions which in turn corresponds to thermal gradient betweenthe MEMS layer to the substrate layer. Different degrees of thermalgradient may in turn correspond to a different degree of offset in thelocation in the proof mass due to thermal gradient. In order to capturethe z-axis thermal gradient that is relevant to z-axis proof massoffset, in some embodiments the temperature may be located andconfigured such that other thermal gradients (e.g., in-plane within theCMOS layer) are rejected. Based on a correspondence between the z-axisthermal gradient and the offset, compensation may be applied to moreaccurately capture the actual z-axis linear acceleration in the presenceof a z-axis thermal gradient.

Within the substrate layer 206, the response of the temperature sensorsdue to the z-axis temperature gradient TGz transferred through theanchors will be greatest at temperature sensor 260B and 266B directlybelow the anchors and decrease in temperature as the thermal gradientdissipates outward. Temperature sensors 260A/260C/266A/266C may beslightly offset from anchors 214 and 216 and output values indicative ofthe dispersion of heat from the anchors to through the material of thesubstrate layer 206. The heat dispersion to the other temperaturesensors will be reduced the further away that the temperature sensor isfrom the anchors 214 and 216, with sensors located between the anchors214 and 216 (e.g., temperature sensors 272A/272B, 262A/262B, 264A/264B,and 274A/274B) experiencing substantial changes in temperature due toheat dispersion from both anchors. Although the thermal gradient fromelectrodes 240/242/244/246 is likely to be substantially less than thethermal gradient from anchors 214/216, heat may dissipate from theelectrodes in a similar manner. Z-axis temperature gradients may also betransferred to the substrate layer 206 via outer walls of the MEMSdevice (e.g., directly from MEMS layer 204 to substrate layer 206 viabonding 208B), in which case z-axis thermal gradients may be experiencedby the temperature sensors within the substrate layer in a similarmanner to x-axis and or y-axis thermal gradients (e.g., as a heat sourceapplied from the side of the substrate layer 206).

The temperature sensors within the substrate layer may also havedifferent outputs based on the z-axis location of the temperaturesensors within the substrate layer 206 (e.g., outputs from temperaturesensors 270A/270B, 272A/272B, 274A/274B, and 276A/276B may also bereduced based on dispersion in heat along the z-axis). The outputs ofthe temperature sensors may be substantially different in the presenceof a z-axis thermal gradient in the positive z-direction (e.g., from aheat source applied below the substrate layer 206). In contrast to athermal gradient applied via the MEMS layer 204, the temperature sensorswithin the substrate layer 206 should have substantially similar values,with temperature sensors located closer to the bottom of the substratelayer 206 (e.g., temperature sensors 270A/270B, 272A/272B, 274A/274B,and 276A/276B) experiencing larger relative changes in output comparedto temperature sensors located closer to the top of the substrate layer206 (e.g., temperature sensors 260A/260B/260C, 262A/262B, 264A/264B, and266A/266B/266C). Such a temperature gradient may also be identifiablebecause there should not be a significant difference in temperaturesensed proximate to the anchors as compared to other sensors within thesame x-y plane of the substrate layer.

The outputs of the temperature sensors may be provided to processingcircuitry for additional processing. The temperature sensor outputs maybe provided to the processing circuitry by any suitable form oftransmission, such as by wirebonds, vias, or other suitable electricaltransmission paths. In some embodiments, some or all of the processingcircuitry utilized to initially process the temperature sensor outputsmay be included within the MEMS device 200, while in some embodimentssome or all of the processing may be performed by external circuitrysuch as a microprocessor that receives data via a wired or wireless datapath. In the exemplary embodiment of FIGS. 2A and 2B, the processingcircuitry may be included in the CMOS substrate layer 206, withtemperature sensor outputs from temperature sensors within the CMOSsubstrate layer 206 processed via internal electrical connections (notdepicted) and other temperature sensors outputs (e.g., of temperaturesensors 250, 252, 254, and 256) provided to the processing circuitry viawire bonds to the CMOS substrate layer 206 (not depicted).

The temperature sensor outputs may be analyzed by the processingcircuitry to identify thermal gradients of interest. As describedherein, the absolute values of temperature sensor outputs and rate ofchange of temperature sensor outputs may provide detailed informationabout the location of the heat source (e.g., applied at which layer ofthe MEMS device, applied at which side of the MEMS device, and extent ofoverlap between the heat source and the MEMS device), the intensity ofthe heat source (e.g., based on relative temperature sensor outputs,rate of change of outputs proximate the heat source, etc.), and patternof application (e.g., heat sources applied in a periodic manner, aspulses, or in other patterns, versus heat sources that have minimalvariation). In some embodiments, respective temperature sensor outputs(e.g., along axes within an x-y plane to identify lateral thermalgradients, at different depths/planes to identify vertical and/orlateral thermal gradients, or at relative locations with respect to acenter point and anchor as described with respect to FIGS. 3A-3C forrejecting lateral thermal gradients while measuring vertical thermalgradients) may be coupled to circuitry such as resistive bridges (e.g.,with temperature sensors as one or more of the resistances) such thatrelative differences in temperature sensor outputs may be quicklydetermined by a single output value. In some embodiments, differentsubsets of temperature sensors may be of different types, for example,having different accuracy or response time.

In some embodiments, one or more switching elements (e.g., switches,transistors, MOSFETS, etc.) may selectively change the temperaturesensors being monitored and/or selectively combine temperature sensoroutputs (e.g., as provided to bridges as described herein) to measureparticular temperature characteristics. For example, in some embodimentsa subset of the temperature sensors may be switched such that they arelocated in a particular manner as described herein to reject lateralthermal gradients and/or induced strain on the sensor (e.g., to identifyperpendicular thermal gradients). Other temperature sensors may beswitched such that they measure lateral thermal gradient, intentionallyidentify strain effects, measure absolute temperature, or suitablecombinations thereof.

A thermal gradient may alter the offset and sensitivity of the MEMSdevice. Operation of the MEMS device depends on movement of the physicalcomponents and measurement of the accelerometer is taken in reference toa reference state. Thermal gradients may create Knudsen forces andnon-homogenous changes in air pressure, e.g., based on differenttemperatures and pressures within the cavity. The creation of Knudsenforces may cause suspended components of the device (e.g., proof masses222/224/226/228) to move absent any applied external force (e.g., theproof masses move to a new reference state when the MEMS device issupposed to be in a reference state and stationary). The changes in airpressure may cause a similar movement to the suspended proof massesbecause forces result from the air pressure that are applied to theproof masses. Movement of the proof masses during reference state isundesired because it adds a component to the measured value output thatis not due to force being measured. When the reference state capacitancebetween a portion of a proof mass and an electrode is a known value, theunknown measured value is determined using this known value and a changein capacitance from the known value. On the other hand, when Knudsenforces or other changes to the location of the proof masses relative tothe electrodes due to thermal gradients skew the reference statecapacitance value, the accuracy of the determination of measured forceis affected.

In some embodiments, the processing circuitry may also receiveadditional external data relating to heat sources. For example, theprocessing circuitry may be in communication with other circuitry suchas external processors, batteries, displays, transponders, or othertemperature measurement circuitry of the end-use device in which theMEMS device is incorporate. Information about the operation of thesecomponents may be provided to the processing circuitry. In someembodiments, such information may be correlated with temperature sensormeasurements of the MEMS device to identify patterns of heat dispersionfrom other components and systems of the end-use device. Thisinformation may be used to proactively perform compensation such as bymodifying the operation of the MEMS device prior to thermal gradientsfrom the heat source actually affecting the output of the MEMS device.Information from the MEMS device may also be provided to the othercomponents and systems of the MEMS device, for example, to betteridentify patterns of thermal gradient within the end-use device andmodify operations of the end-use device as appropriate (e.g., modifyingoperating voltages, processing loads, entering low power or sleep modes,etc.).

Once temperature sensor outputs and other related values (e.g., combinedoutputs based on bridge circuits, etc.) have been received, theprocessing circuitry may respond to the measured temperatureinformation. One exemplary response may be to compensate for temperaturegradients based on changing scaling factors for MEMS device outputs.Calibration testing may be performed during manufacturing or in thefield, that may determine changes in MEMS device outputs based ondifferent thermal gradients (e.g., location, degree, pattern). Thisinformation may be stored (e.g., in a lookup table stored at the MEMSdevice) such that additive compensation and/or scaling factors may beapplied to maintain correct output values (e.g., linear acceleration,angular velocity, etc.) in the presence of thermal gradients. Anotherexemplary response may be to modify the operation of the MEMS device.Applied signals such as signals that cause movement of MEMS components(e.g., a drive signal of a MEMS gyroscope) or that are transmitted viaproof masses and electrodes (e.g., a sense signal of a MEMSaccelerometer or pressure sensor) may be modified based on knowntemperature effects (e.g., increasing or inhibiting movement ofcomponents of a suspended spring-mass system) determined, for example,based on a calibration routine. Another exemplary response may be tomodify the operation of the MEMS device as a whole, for example, byplacing the sensor in a temporary sleep mode, modifying parameters of apower source for the MEMS device, or otherwise changing the overallusage of the MEMS device. Another exemplary response may be to providenotifications and alerts to other components and systems of the end-usedevice, such that those components or systems are aware that valuesoutput by the MEMS device may be partially compromised versus normaloutput values. The notifications and alerts may provide informationabout the heat source, which may permit the other components and systemsto modify their operation to reduce the severity of the thermalgradients experienced by the MEMS device. In some embodiments, thenotification or alert may request that specific steps be taken by othercomponents and systems. In some embodiments, the notification mayprovide information about the heat source or thermal gradient that canbe used by the external system to modify their operation.

FIGS. 3A-3C show exemplary temperature sensing configurations inaccordance with some embodiments of the present disclosure. As describedherein, within a particular layer (e.g., substrate layer 206) there maybe a limited number of locations at which a substantial heat source maybe applied to the layer. In the exemplary embodiment of substrate 206 ofFIGS. 2A-2B and 3A-3C, those locations may correspond to the sides ofthe substrate 206 (e.g., left-side or negative y-side, right-side orpositive y-side, top-side or positive x-side, bottom-side or negativex-side), the lower surface of the substrate layer 206 (e.g., lower x-yplane of FIG. 2A, not depicted in FIG. 2B and FIGS. 3A-3C), and theupper cavity-facing surface of substrate layer 206 (e.g., withsubstantial heat sources corresponding to the anchoring locations 214and 216, as well as the bonding points to the MEMS layer along thepreviously-described sides that form the cavity (depicted in FIG. 2A).

In the exemplary embodiments of FIGS. 2A-2B and FIGS. 3A-3C, thestructure may be symmetric about a center point with respect to the heatsources. Whether or not such symmetry exists in other MEMS devicedesigns, it may also be possible to identify center point locationswhere heat sources are balanced with respect to their potentialcontribution to the overall thermal behavior at the center point.Combinations of temperature sensors may then be identified that allowfor the rejection of some thermal gradients in order to isolatecontributions from particular thermal gradients of interest. In theexemplary embodiments of FIGS. 3A-3C, temperature sensor locations maybe identified to reject thermal gradients in the x-y plane due to heatsources applied at the side of the substrate layer 206, in order toisolate a thermal gradient received at the substrate layer 206 from MEMSlayer 204 via anchoring locations 214 and 216. For example, some MEMSdevices may be particularly sensitive to z-axis thermal gradients thatcause relative movement (i.e., not due to a force to be measured)between portions of the MEMS layer 204 and the substrate layer 206.

FIG. 3A shows an exemplary temperature sensing configuration forrejecting x-y plane thermal gradients from while identifying z-axisthermal gradients received via anchoring locations 214 and 216. In theexemplary embodiment of FIG. 3A, temperature sensors 260B and 266B alongmeasurement axis 304 may be utilized with temperature sensors 264A and262B along measurement axis 306 and/or temperature sensors 262A and 264Balong measurement axis 308. The measurement axes may cross at centerpoint 302. The sensors along measurement axis 304 are located at theanchoring locations 214 and 216 while the temperature sensors alongmeasurement axis 306 and 308 are located at identical respective x-ydistances from the anchoring locations 214 and 216, such that heatreceived from the MEMS layer 204 via anchoring locations 214 and 216will propagate to these temperature sensors in a similar manner. In thismanner, the response of the temperature sensors along measurement axis304, 306, and 308 to the z-axis thermal gradient should be correlated(e.g., in proportion to the respective distance from the anchors). Onthe other hand, thermal gradients from other heat sources (e.g., alongthe sides of the substrate layer 206) will be experienced in adifferential manner by the sensors, based on their respective locationwith respect to the side where the heat source is applied.

The distances between respective sensors along these axes are identical(e.g., the x-axis distance between temperature sensor 260B totemperature sensors 262A and 262B is identical to the x-axis distancebetween temperature sensor 266B to temperature sensors 264A and 264B,the x-axis distance between temperature sensor 260B to temperaturesensors 264A and 264B is identical to the x-axis distance betweentemperature sensor 266B to temperature sensors 262A and 262B, the y-axisdistance between temperature sensor 260B to temperature sensors 262B and264B is identical to the y-axis distance between temperature sensor 266Bto temperature sensors 262A and 264A, and the y-axis distance betweentemperature sensor 260B to temperature sensors 262A and 264A isidentical to the y-axis distance between temperature sensor 266B totemperature sensors 262B and 264B). The outputs of the sensors can beanalyzed (e.g., as depicted and described in a bridge configuration ofFIG. 4 ) such that thermal gradients from heat sources along the sidesof the substrate layer 206 effectively cancel, while the thermalgradients along the z-axis are additive and are provided as an output.

For example, because temperature sensors 262A, 262B, 264A, and 264C arelocated away from the anchors 214 and 216, temperatures measured by themare impacted by dispersion of heat from anchors 214 and 216 throughsubstrate layer 206, as well as other lateral thermal gradients withinthe substrate layer 206 such as x-axis thermal gradient TGx, y-axisthermal gradient TGy, or an in-plane thermal gradient having both x-axisand y-axis components. For example, in addition to heat dispersion alongthe z-axis from the MEMS layer through the anchors 214 and 216dispersion of heat in-plane as a lateral thermal gradient, the substratelayer 206 may also experience thermal gradients due to an adjacent heatsource that also creates a lateral thermal gradient. As describedherein, the primary concern for the many MEMS devices may be z-axisthermal gradients. Accordingly, as described herein, temperature sensorsmay be located at respective locations within the x-y plane of thesubstrate layer 206 in order to reject the effect of lateral thermalgradients due to lateral heat sources (and lateral thermal gradientscaused by dispersion from anchors 014 and 216) while isolating only thez-axis thermal gradient.

In an embodiment, the temperature sensors are located at specificrelative locations in order to reject lateral thermal gradients due tolateral heat sources, and also to counteract any changes in temperatureresponse due to any induced strain effects. The temperature sensors262A/264B and 264A/262B may be located at equivalent distancesrespective to associated temperature sensors 260B and 266B. Thetemperature sensors are further placed about a center point within thesubstrate layer with respect to the anchoring regions 214 and 216. Inparticular, a first distance between temperature sensor 262A and centerpoint 302 is the same distance between temperature sensor 264B andcenter point 302. Similarly, a second distance between temperaturesensor 264A and center point 302 is the same distance betweentemperature sensor 262B and center point 302. A third distance betweentemperature sensor 260B and center point 302 is the same distancebetween temperature sensor 266B and center point 302, though this may bedifferent from the first and second distances. The temperature sensorsare symmetric to one another about the center point 302. In this manner,when a strain is induced on the temperature sensors, the resultingchanges of output values of each of the temperature sensors are similarand balanced, resulting in the rejection of strain effects on theoverall output signal.

In response to a thermal gradient in the z axis and absence of a lateralthermal gradient applied by lateral heat sources (and assuming no strainor other effects), temperature sensors 260B and 266B will have a similarresponse, since each is located at an equivalent location below theirrespective anchoring regions 214 and 216. Similarly, in the absence of alateral thermal gradient applied by lateral heat sources (and assumingno strain or other effects), the only source of heat dispersion totemperature sensors 262A/264A/262B/264B is the in-plane temperaturedistribution within the substrate layer 206 due to heat dispersion fromanchoring regions 214 and 216 in response to the z-axis thermalgradient. Because the temperature sensors 262A/264A/262B/264B areequidistant from the anchoring regions 214 and 216, they will have asimilar response due to the in-plane temperature distribution from theanchoring regions. In this manner, the output at the temperaturessensors 260B, 266B, and 262A/264A/262B/264B due to the z-axis thermalgradient may be additive based on the relative placement of thetemperature sensors (e.g., two under the anchoring regions, two or fourremote from the anchoring regions, with the temperature sensors balancedand equidistant about a center point between the anchoring regions andaligned along axes about center point).

In the presence of a lateral thermal gradient within the substrate layer206 due to a lateral heat source, the lateral thermal gradient maydisperse through the substrate layer 206 within the plane of thetemperature sensors in the x-direction and/or y-direction based on thelocation of the heat source. For example, the presence of a heat sourcealong the right-hand side (i.e., in the positive y direction) and a coldsource along the left-hand side (i.e., in the negative y direction) ofthe substrate 206 may disperse heat from left to right as depicted bythermal gradient TGx in FIG. 3 , with the temperature change sensed bythe temperature sensors 262A/264B and 262A/264A being equal and oppositein magnitude, with relatively larger temperature changes at each oftemperature sensors 260B and 266B due to the thermal gradient TGx. Thepresence of a heat source along the top side (i.e., in the positive xdirection) and a cold source along the bottom side (i.e., in thenegative x direction) of the substrate layer 206 may disperse heat frombottom-to-top as depicted by thermal gradient TGx in FIG. 4 , with thetemperature change sensed by the temperature sensors 262A/264B and262A/264A being equal and opposite in magnitude, with relatively smallertemperature changes at each of temperature sensors 260B and 266B due tothe thermal gradient TGx.

Lateral thermal gradients may also be applied in both the x directionand y direction at the same time, for example, from multiple heatsources located adjacent to the substrate layer 206 of the MEMSaccelerometer or a point heat source that distributes in multipledirections. However, in all instances the lateral thermal gradients fromadjacent heat sources (e.g., with the exception of lateral thermalgradients from dispersion of heat from the anchoring region) may beapplied at a side of the substrate layer 206 and then dispersethroughout the substrate layer in a manner that results in differentialtemperature changes between the temperature sensors. In contrast, as aresult of the relative locations of the temperature sensors 260B, 266B,and 262A/262B/264A/264B, a z-axis thermal gradient applied to theanchoring region will result in equivalent increases in temperature attemperature sensors 260B and 266B and at temperature sensors262A/262B/264A/264B, respectively. Accordingly, the relative temperaturesensed by these temperature sensors may be used to distinguish changesin temperature due to z-axis thermal gradient (i.e., evidenced byequivalent temperature changes at the thermistors) and changes intemperature due to lateral thermal gradients (i.e., evidenced bydiffering changes in temperature at the temperature sensors based on thelocation of the lateral heat source)

FIGS. 3B and 3C show additional exemplary configurations of temperaturesensors for rejecting x-y plane thermal gradients while accentuatingz-axis thermal gradients received via the anchoring locations.Consistent with the description of FIG. 3A, temperature sensors areselected based on configurations that provide additive responses to thez-axis thermal gradient received via anchoring regions 214 and 216 andproportional and differential responses to other thermal gradients. Inthe exemplary embodiment of FIG. 3B, some of the respective measurementaxes may be orthogonal to each other, such as measurement axes 312 and316 and measurement axes 314 and 318. In the exemplary embodiment ofFIG. 3C, some of the temperature sensors (e.g., temperature sensors 276Aand 270B along measurement axis 324 and temperature sensors 270A and276B along measurement axis 322) may be located on an x-y plane beneaththe temperature sensors that are proximate to the anchoring locations214 and 216.

In an exemplary embodiment, temperature outputs from the thermistors maybe processed using a bridge configuration, such as a Wheatstone bridgeconfiguration, as will be discussed further in the description for FIG.4 . FIG. 4 shows exemplary Wheatstone bridge processing circuitry inaccordance with some embodiments of the present disclosure. Theexemplary configuration of FIG. 4 , when used with temperature sensors(e.g., thermistors) located as described herein and depicted in FIGS.3A-3C, may enable the accurate measurement of a vertical thermalgradient (e.g., a Vout value 412) while rejecting effects of strain andlateral thermal gradients from adjacent heat sources. Althoughthermistors are depicted in FIG. 4 , it will be understood that othertypes of temperature sensors (e.g., BJTs or MOSFETs) or combinationsthereof may be utilized in the Wheatstone bridge arrangement describedherein.

FIG. 4 shows illustrative temperature measurement configuration 400 inaccordance with some embodiments of the present disclosure. Temperaturemeasurement configuration 400 arranges thermistors 402, 404, 406, and408 in a Wheatstone bridge configuration. Because the resistance ofthermistors is temperature-dependent, measuring the resistances at thethermistors provides an estimate of the corresponding temperatures.Voltage 410, a known voltage Vin, is applied to the Wheatstone bridgeand voltage 412, a measured voltage Vout, is used to determine an outputthat changes in proportion to the z-axis thermal gradient applied at theanchoring regions.

Consider four resistances R₄₀₂, R₄₀₄, R₄₀₆, and R₄₀₈ corresponding tofour thermistors 402, 404, 406, and 408 at temperatures t₄₀₂, t₄₀₄,t₄₀₆, and t₄₀₈, respectively. Resistances R₄₀₂, R₄₀₄, R₄₀₆, and R₄₀₈ areproportional to temperatures t₄₀₂, t₄₀₄, t₄₀₆, and t₄₀₈ according to thedesign of the thermistors. Accordingly, variations in temperature resultin changes to resistance, which in turn, changes the output voltage.Thus, the output voltage 412 (Vout) is equal the difference betweenvoltage at the node A between thermistor 402 and thermistor 408 (i.e.,input voltage Vin*R₄₀₂/(R₄₀₂+R₄₀₈)) and the voltage at the node Bbetween thermistor 404 and thermistor 406 (i.e., input voltageVin*R₄₀₄/(R₄₀₆+R₄₀₄)).

In an embodiment of the present disclosure, thermistor 402 maycorrespond to a first thermistor remote from the anchors, thermistor 406may correspond to a thermistor located along a common measurement axison the opposite side of the center point 302 from thermistor 402,thermistor 404 may correspond to a thermistor located proximate one ofthe anchoring locations, and thermistor 408 may correspond to athermistor proximate the other anchor and located along a commonmeasurement axis on the opposite side of the center point 302 fromthermistor 406. In response to no temperature gradient, all of thethermistors (e.g., assuming that the thermistors have identical valuesand temperature responses) should be at the same temperature and thuswill have identical resistances. The voltage at node A will be one halfof the input voltage Vin, as will the voltage at node B. Thus, theoutput voltage Vout will be zero. When a z-axis thermal gradient isapplied to the anchoring regions, the thermistors located below theanchoring regions (e.g., thermistors 404 and 408) may experience asubstantial change (e.g., decrease) in resistance due to exposure to thethermal gradient, while the change (e.g., reduction) in resistance ofthe thermistors located away from the anchoring regions (i.e.,thermistors 402 and 406) may be significantly less substantial. Thus,the voltage at node A will increase due to the R₄₀₂ having a relativelylarge value as compared to R₄₀₈ while the voltage at node B willdecrease due to the R₄₀₆ having a relatively large value as compared toR₄₀₄. Because thermistors 404 and 408 change resistance in the samemanner, and thermistors 402 and 406 change resistance in the samemanner, the increase in the voltage at node A and the decrease in thevoltage at node B are proportional. In this manner, Vout increases asthe vertical thermal gradient increases and reduces to zero as thevertical thermal gradient decreases.

The thermistor configurations of FIGS. 3A-3C and their processing in theWheatstone bridge of FIG. 4 may also reject lateral thermal gradientsdue to adjacent heat sources. For example, if a heat source is appliedat the left side of the substrate layer 206 and a cold source on theopposite side, resulting in a thermal gradient in the directionindicated by TGx, the temperature at each of the thermistors 402-408will increase, but in different proportions. For example, thetemperature of thermistor 404 will feature the greatest change inresistance (e.g., a decrease resulting from the greatest relativeincrease in temperature), the temperature of thermistor 406 will featurethe second greatest change in resistance (e.g., a decrease resultingfrom the second greatest relative increase in temperature), thetemperature of thermistor 402 will feature the third greatest change inresistance (e.g., a decrease resulting from the third greatest relativeincrease in temperature), and the temperature of thermistor 408 willfeature the least change in resistance (e.g., a decrease resulting fromthe least relative increase in temperature). Because the x-axis distancebetween thermistor 404 and thermistor 406 is the same as the x-axisdistance between thermistor 402 and thermistor 408, the relative changein resistance of thermistor 404 compared to thermistor 406 is the sameas the relative change in resistance of thermistor 402 compared tothermistor 408 (i.e., with thermistor 404 and 402 experiencingproportionally larger changes in resistance compared to thermistor 402and 408). Thus, while the voltages at nodes A and B change as a resultof the lateral thermal gradient, they change in the same manner suchthat Vout remains zero. The thermistor configuration of FIG. 4 similarlyrejects lateral thermal gradients along the x-axis (e.g., applied to thetop or bottom side of the substrate layer 206).

FIG. 5 shows exemplary steps for processing received temperature sensoroutputs in accordance with some embodiments of the present disclosure.Although FIG. 5 is described in the context of the present disclosure,it will be understood that the methods and steps described in FIG. 5 maybe applied to a variety of MEMS device designs, temperatures sensortypes, processing circuitry, and compensation techniques. Although aparticular order and flow of steps is depicted in FIG. 5 , it will beunderstood that in some embodiments one or more of the steps may bemodified, moved, removed, or added, and that the flow depicted in FIG. 5may be modified.

At step 502, temperature sensor outputs may be received (e.g., byprocessing circuitry of the MEMS device) from temperature sensorslocated on and/or within one or more layers of the MEMS device. Thetemperature sensor outputs may be received over time, such that patternsand changes in temperature may be identified. In some embodiments, thetemperature sensor outputs may be taken at particular stages in sensoroperation, such as at power up, initiation of measurements, periodicallyduring MEMS device operation, and prior to shut down. In someembodiments (not depicted in FIG. 5 ), information from other devices,components and sensors may also be acquired (e.g., relating to operationof adjacent components, external temperature measurements, powerconsumption, etc.). Once the temperature sensor outputs are received,processing may continue to step 504.

At step 504, the temperature sensor outputs may be processed.Temperature sensor outputs may be processed individually, for example,with filters to remove noise from temperature sensor outputs andamplifiers, A/D converters, and other suitable components to provideappropriate scaling for further analysis. In some embodiments, multipletemperature sensor outputs may be processed together, for example, bybridges such as Wheatstone bridges as described herein. Once thetemperature sensor outputs are processed for further analysis,processing may continue to step 506.

At step 506, thermal gradients may be calculated based on the receivedvalues. As described herein, by having multiple temperature sensors atparticular locations with respect to heat sources and, in someembodiments, at different layers or depths within layers, absolutetemperatures at particular locations temperature differences betweendifferent locations may be identified. Rates of change of thermalgradients may also be determined based on thermal gradient informationover time. Once the thermal gradients have been calculated, processingmay continue to step 508.

At step 508, the thermal gradients may analyzed to determine whethersome form of action should be taken. In some embodiments, tolerances maybe associated with absolute temperature at particular locations, numberof temperature sensors identifying an absolute temperature abovethreshold values, temperature differences between particular temperaturesensor locations, number of temperature differences exceeding thresholdvalues, and rate of change of absolute temperatures values and/ortemperature difference values. In some embodiments, a heat source may beidentified based on the thermal gradient information, for example, byidentifying a location of the heat source and a pattern of application.This heat source identification may be compared to known heat sourcelocations and patterns, as well as data received from other sources(e.g., external temperature sensor data or information about operationof other components or devices). Once the thermal gradients areanalyzed, processing may continue to step 510.

At step 510, it may be determined (e.g., by processing circuitry)whether an error that requires additional action has been identified. Ifno additional action is required, processing may return to step 502 toreceive additional temperature sensor outputs. If additional action isrequired, the additional action may be identified based on the type andseverity of error that is identified. Processing may then continue tostep 512.

At step 512, it may be determined whether the MEMS device may continueoperation in spite of the error. In some embodiments, thermal gradientsthat indicate errors but with characteristics (e.g., absolutetemperature, temperature difference, rate of change) that fall belowcertain thresholds and thus may require only notifications ormodifications to operation of the MEMS device, while more severe errorsmay require partial or complete shutdown of the MEMS device. If the MEMSdevice may continue operation, processing may continue to step 514. Ifthe MEMS device may not continue operation, processing may end.

At step 514, notifications may be provided and/or the operations of theMEMS device may be modified to continue operation despite the identifiederror. Notifications may be internal to the MEMS device and/or may beprovide to external components and devices, and may provide informationabout the nature and severity of the error, and any corrective actiontaken by the MEMS device or to be taken by other components and devices(e.g., modifying an accuracy of the output of the MEMS device). In someembodiments, the notification may include requests or instructions toreduce or mitigate heat dispersion from the heat source, for example, bymodifying operation of an external component or device. Modifications tothe operation of the MEMS device may include a variety of modificationsas described herein, such as modification of scaling factors, changes tocalculation of measured parameters, and modification of operatingparameters of the MEMS device (e.g., drive voltages, sense voltages,etc.). Once notifications have been provided and/or operations of thesensor have been modified, processing may return to step 502 to receiveadditional temperature sensor outputs.

The foregoing description includes exemplary embodiments in accordancewith the present disclosure. These examples are provided for purposes ofillustration only, and not for purposes of limitation. It will beunderstood that the present disclosure may be implemented in formsdifferent from those explicitly described and depicted herein and thatvarious modifications, optimizations, and variations may be implementedby a person of ordinary skill in the present art, consistent with thefollowing claims.

What is claimed is:
 1. A microelectromechanical (MEMS) device,comprising: a layer; a plurality of temperature sensors located withinthe layer, comprising; a first temperature sensor at a first locationrelative to a center point within the layer, wherein a first response ofthe first temperature sensor changes based on a temperature at the firstlocation; a second temperature sensor at a second location relative tothe center point, wherein the second location is on a first commonmeasurement axis on an opposite side of the center point from the firstlocation, and wherein a second response of the second temperature sensorchanges based on a temperature at the second location; a thirdtemperature sensor at a third location relative to the center point,wherein a third response of the third temperature sensor changes basedon a temperature at the third location, and wherein a first output valueis based on the first response and the third response; and a fourthtemperature sensor at a fourth location relative to the center point,wherein the fourth location is on a second common measurement axis on anopposite side of the center point from the third location, wherein afourth response of the fourth temperature sensor changes based on atemperature at the fourth location, and wherein a second output value isbased on the second response and the fourth response; and processingcircuitry configured to output a signal that corresponds to a verticalthermal gradient perpendicular to the layer based on a change in adifference between the first output value and the second output value inresponse to the vertical thermal gradient, and wherein the processingcircuitry rejects a lateral thermal gradient within the layer inoutputting the signal.
 2. The MEMS device of claim 1, wherein the layercomprises a first layer, further comprising at least one anchor and asecond layer, wherein the at least one anchor couples the first layer tothe second layer.
 3. The MEMS device of claim 2, wherein the at leastone anchor is located vertically above the center point.
 4. The MEMSdevice of claim 2, wherein the at least one anchor comprises a pluralityof anchors each located equidistant from the center point.
 5. The MEMSdevice of claim 2, further comprising a gap between the first layer andthe second layer, wherein the at least one anchor is located within thegap.
 6. The MEMS device of claim 2, wherein a first anchor of the atleast one anchor is in contact with the first layer at a first anchoringlocation, wherein the third temperature sensor of the plurality oftemperature sensors is located below the first anchoring location,wherein a second anchor of the at least one anchor is in contact withthe first layer at a second anchoring location, wherein the fourthtemperature sensor of the plurality of temperature sensors is locatedbelow the second anchoring location, and wherein the first and thesecond temperature sensors of the plurality of temperature sensors arenot located below the first or the second anchoring locations.
 7. TheMEMS device of claim 1, wherein the layer comprises a first layer,further comprising a second layer, wherein the first layer comprises afirst plane located within the first layer, wherein the second layercomprises a second plane located within the second layer, and whereineach of the plurality of temperature sensors is located within the firstplane.
 8. The MEMS device of claim 7, wherein the first plane isparallel to the second plane.
 9. The MEMS device of claim 1, wherein thelayer comprises a first layer, further comprising a second layer,wherein the second layer comprises a MEMS layer and the first layercomprises a CMOS layer.
 10. The MEMS device of claim 1, wherein thefirst common measurement axis and the second common measurement axis areorthogonal axes.
 11. The MEMS device of claim 1, wherein a respectiveoutput from one or more of the plurality of temperature sensors changesbased on a strain induced on the one or more of the plurality oftemperature sensors, and wherein, in response to the strain induced onthe one or more of the plurality of temperature sensors, the signal issubstantially unchanged.
 12. The MEMS device of claim 11, wherein theone or more of the plurality of temperature sensors comprise at leasttwo temperature sensors, and wherein, in response to the strain inducedon the one or more of the plurality of temperature sensors, the signalis substantially unchanged based on the two temperature sensors beingequidistant from a center point within the layer.
 13. The MEMS device ofclaim 1, wherein a respective output from one or more of the pluralityof temperature sensors changes based on a strain induced on the one ormore of the plurality of temperature sensors, and wherein the signalchanges in response to the strain induced on the one or more of theplurality of temperature sensors.
 14. The MEMS device of claim 1,wherein the plurality of temperature sensors comprises BJTs, MOSFETs, orthermistors.
 15. The MEMS device of claim 1, wherein the plurality oftemperature sensors is configured in a Wheatstone bridge, and whereinthe processing circuitry is coupled to the plurality of temperaturesensors via the Wheatstone bridge.
 16. The MEMS device of claim 1,further comprising one or more switching elements to select a subset ofthe plurality of temperature sensors to reconfigure the signal to changein response to one of a thermal gradient perpendicular to the layer, athermal gradient parallel to the layer, an induced strain, or atemperature value.
 17. The MEMS device of claim 1, wherein the MEMSdevice comprises an accelerometer, a gyroscope, a magnetometer, abarometer, a microphone, or an ultrasonic sensor.
 18. The MEMS device ofclaim 1, wherein the processing circuitry rejects any lateral thermalgradient within the layer based on a proportional response of the firstoutput value and the second output value to the lateral thermalgradient.
 19. The MEMS device of claim 1, wherein the respectiveresponses of the plurality of temperature sensors correspond to changesin current, voltage, or resistance.
 20. A substrate of amicroelectromechanical (MEMS) device, comprising: a plurality oftemperature sensors located within the substrate, comprising; a firsttemperature sensor at a first location relative to a center point withinthe substrate, wherein a first response of the first temperature sensorchanges based on a temperature at the first location; a secondtemperature sensor at a second location relative to the center point,wherein the second location is on a first common measurement axis on anopposite side of the center point from the first location, and wherein asecond response of the second temperature sensor changes based on atemperature at the second location; a third temperature sensor at athird location relative to the center point, wherein a third response ofthe third temperature sensor changes based on a temperature at the thirdlocation, and wherein a first output value is based on the firstresponse and the third response; and a fourth temperature sensor at afourth location relative to the center point, wherein the fourthlocation is on a second common measurement axis on an opposite side ofthe center point from the third location, wherein a fourth response ofthe fourth temperature sensor changes based on a temperature at thefourth location, and wherein a second output value is based on thesecond response and the fourth response; and processing circuitryconfigured to output a signal that corresponds to a vertical thermalgradient perpendicular to the substrate based on a change in adifference between the first output value and the second output value inresponse to the vertical thermal gradient, and wherein the processingcircuitry rejects a lateral thermal gradient within the substrate inoutputting the signal.
 21. A method for operating amicroelectromechanical (MEMS) device, comprising: generating, by a firsttemperature sensor, a first temperature signal at a first locationrelative to a center point within a substrate layer of the MEMS device,wherein the first temperature signal of the first temperature sensorchanges based on a temperature at the first location; generating, by asecond temperature sensor, a second temperature signal at a secondlocation relative to the center point, wherein the second location is ona first common measurement axis on an opposite side of the center pointfrom the first location, and wherein the second temperature signal ofthe second temperature sensor changes based on a temperature at thesecond location; generating, by a third temperature sensor, a thirdtemperature signal at a third location relative to the center point,wherein the third temperature signal of the third temperature sensorchanges based on a temperature at the third location; generating, by afourth temperature sensor, a fourth temperature signal at a fourthlocation relative to the center point, wherein the fourth location is ona second common measurement axis on an opposite side of the center pointfrom the third location, and wherein the fourth temperature signal ofthe fourth temperature sensor changes based on a temperature at thefourth location; generating, by processing circuitry, a first outputvalue based on the first temperature signal and the third temperaturesignal; generating, by the processing circuitry, a second output valuebased on the second temperature signal and the fourth temperaturesignal; and outputting, by the processing circuitry, a signal thatcorresponds to a vertical thermal gradient perpendicular to thesubstrate layer based on a change in a difference between the firstoutput value and the second output value in response to the verticalthermal gradient, wherein the processing circuitry rejects a lateralthermal gradient within the substrate layer in outputting the signal.